Problem: Solve for $x$ and $y$ using elimination. ${-3x-5y = -52}$ ${4x+4y = 48}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $4$ and the bottom equation by $3$ ${-12x-20y = -208}$ $12x+12y = 144$ Add the top and bottom equations together. $-8y = -64$ $\dfrac{-8y}{{-8}} = \dfrac{-64}{{-8}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-3x-5y = -52}\thinspace$ to find $x$ ${-3x - 5}{(8)}{= -52}$ $-3x-40 = -52$ $-3x-40{+40} = -52{+40}$ $-3x = -12$ $\dfrac{-3x}{{-3}} = \dfrac{-12}{{-3}}$ ${x = 4}$ You can also plug ${y = 8}$ into $\thinspace {4x+4y = 48}\thinspace$ and get the same answer for $x$ : ${4x + 4}{(8)}{= 48}$ ${x = 4}$